Conic Sections Case Study Questions Class 11 Maths Chapter 10

Download CBSE and ICSE Books in PDF Format

Reading Time: 6 minutes

Hello students, we are providing case study questions for class 11 Maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 11 Maths. In this article, you will find case study questions for cbse class 11 Maths chapter 10 Conic Sections.

Chapter	Conic Sections
Type of Questions	Case Study Questions
Nature of Questions	Competency Based Questions
Board	CBSE
Class	11
Subject	Maths
Useful for	Class 12 Studying Students
Answers provided	Yes
Difficulty level	Mentioned
Important Link	Class 11 Maths Chapterwise Case Study

Table of Contents

Case Study Questions on Conic Sections

Customised Study Materials for Teachers, Schools and Coaching Institute

Case Study:
A city plans to build a walkway in a garden following the arc of a parabola, with entry at point \( A(0, 0) \) and exit at point \( B(4, 4) \). A lamp post is to be installed at point \( C(2, 1) \) on the walkway. The walkway is designed such that it follows the parabola \( y = ax^2 + bx \).

Questions:

Find the equation of the parabola passing through points \( A(0, 0) \), \( B(4, 4) \), and \( C(2, 1) \).
What are the coordinates of the vertex of this parabola?
Determine the focus and the equation of the directrix for this parabola.
Explain a real-world advantage of using a parabolic path in garden design.

Solutions:

1. Equation of the parabola through \( A(0, 0) \), \( B(4, 4) \), and \( C(2, 1) \):

Assume \( y = ax^2 + bx + c \). Since \( A(0, 0) \) is on the curve: \( c = 0 \). For \( B(4, 4) \): \[ 4 = a(16) + b(4) \implies 16a + 4b = 4 \] For \( C(2, 1) \): \[ 1 = a(4) + b(2) \implies 4a + 2b = 1 \] Now, solve: From the second equation: \[ 4a + 2b = 1 \implies 8a + 4b = 2 \] Subtract from the first: \[ (16a + 4b) – (8a + 4b) = 4 – 2 \implies 8a = 2 \implies a = \frac{1}{4} \] Then \( 4a + 2b = 1 \implies 1 + 2b = 1 \implies 2b = 0 \implies b = 0 \). Therefore, the equation is: \[ y = \frac{1}{4}x^2 \]

2. Vertex of the parabola:

Standard form: \( y = ax^2 + bx \). Here \( a = \frac{1}{4},\ b = 0 \): Vertex at \( x_v = -\frac{b}{2a} = 0 \) \[ y_v = \frac{1}{4} \times (0)^2 = 0 \] So, the vertex is \( (0, 0) \).

3. Equation of focus and directrix:

For \( y = \frac{1}{4}x^2 \), compare with \( y = a x^2 \): Focus at \( \left( 0, \frac{1}{4a} \right) = \left( 0, 1 \right) \), since \( \frac{1}{4a} = 1 \) Equation of directrix: \( y = -1 \)

4. Real-world advantage of a parabolic path:
A parabolic walkway provides a gentle, visually pleasing curve, making it accessible and attractive. Parabolic arches and paths evenly distribute loads and stresses, and can offer optimal sightlines and natural drainage in landscape design.

We hope the given case study questions for Conic Sections Class 11 helps you in your learning.

Also check

Topics from which case study questions may be asked

Introduction to Conic Sections
Circle – Standard Equation and Properties
Parabola – Standard Equation, Focus, Directrix, Axis, and Latus Rectum
Ellipse – Standard Equation, Focus, Directrix, Axes, and Latus Rectum
Hyperbola – Standard Equation, Focus, Directrix, Axes, and Latus Rectum
Eccentricity of Conic Sections
Relationship Between General Equation and Standard Forms
Special Cases and Identification of Conics

Frequently Asked Questions (FAQs) on Conic Sections Case Study Questions

Q1: What is a case study question in mathematics?

A1: A case study question in mathematics is a problem or set of problems based on a real-life scenario or application. It requires students to apply their understanding of mathematical concepts to analyze, interpret, and solve the given situation.

Q2: How should students tackle case study questions in exams?

A2: To tackle case study questions effectively, students should:
Read the problem carefully: Understand the scenario and identify the mathematical concepts involved.
Break down the problem: Divide the case study into smaller parts to manage the information better.
Apply relevant formulas and theorems: Use the appropriate mathematical tools to solve each part of the problem.

Q3: Why are case study questions included in the Class 11 Maths curriculum?

A3: Case study questions are included to bridge the gap between theoretical knowledge and practical application. They help students see the relevance of what they are learning and prepare them for real-life situations where they may need to use these mathematical concepts.

Q4: Are there any online resources or tools available for practicing “Conic Sections” case study questions?

A12: We provide case study questions for CBSE Class 11 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.